1. Understand the Ideal Gas Law:
The ideal gas law is a fundamental relationship that describes the behavior of ideal gases. It's expressed as:
* PV = nRT
Where:
* P is the pressure (in atmospheres, ATM)
* V is the volume (in liters, L)
* n is the number of moles
* R is the ideal gas constant (0.0821 L·atm/mol·K)
* T is the temperature (in Kelvin, K)
2. Convert Gauge Pressure to Absolute Pressure:
Gauge pressure measures the pressure relative to atmospheric pressure. To use the ideal gas law, we need absolute pressure.
* Assuming standard atmospheric pressure is 1 ATM, the absolute pressure is:
* Absolute pressure = Gauge pressure + Atmospheric pressure
* Absolute pressure = 2 ATM + 1 ATM = 3 ATM
3. Plug in the Values and Solve for Volume (V):
* P = 3 ATM
* n = 10 moles
* R = 0.0821 L·atm/mol·K
* T = 200 K
Substitute these values into the ideal gas law equation:
(3 ATM) * V = (10 moles) * (0.0821 L·atm/mol·K) * (200 K)
Simplify and solve for V:
V = (10 * 0.0821 * 200) / 3
V ≈ 54.73 L
Therefore, the volume of the gas is approximately 54.73 liters.
